Cover image for Abel's proof : an essay on the sources and meaning of mathematical unsolvability
Abel's proof : an essay on the sources and meaning of mathematical unsolvability
Pesic, Peter.
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Publication Information:
Cambridge, Mass. : MIT Press, [2003]

Physical Description:
viii, 213 pages : illustrations ; 21 cm
The scandal of the irrational -- Controversy and coefficients -- Impossibilities and imaginaries -- Spirals and seashores -- Premonitions and permutations -- Abel's proof -- Abel and Galois -- Seeing symmetries -- The order of things -- Solving the unsolvable.
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QA212 .P47 2003 Adult Non-Fiction Non-Fiction Area

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In 1824 a young Norwegian named Niels Henrik Abel proved conclusively that algebraic equations of the fifth order are not solvable in radicals. In this work, Peter Pesic shows what an important event this was in the history of thought. He also presents it as a remarkable human story. Abel was 21 when he self-published his proof, and he died five years later, poor and depressed, just before it started to receive wide acclaim. Abel's attempts to reach out to the mathematical elite of the day had been spurned, and he was unable to find a position that would allow him to work in peace and marry his fianc e.

Author Notes

Peter Pesic is Tutor and Musician-In-Residence at St. John's College, Santa Fe.

Reviews 1

Choice Review

Certain mathematical achievements exercise a perennial fascination for the public at large, or they should, at any rate. Abel's theorem, that the general quintic equation admits no solution by a formula involving radicals, counts as one of these. Although the story will unfold as one reads deep into any good undergraduate abstract algebra textbook, the thrill-seeker, alas, may find such an itinerary too demanding. Jean-Pierre Tignol's Galois' Theory of Algebraic Equations (CH, Apr'02) offers a streamlined initiation that exploits a little known fact: Abel's original approach, albeit less sophisticated and general than Galois's, also demands much less of the student. Here, Pesic (St. John's College, Santa Fe), addressing a very broad audience, offers a popular, historical account that culminates with an annotated translation of Abel's paper of 1824, available previously only in a flawed translation. Readers unsatisfied by Pesic's short chapter "Solving the Unsolvable" should have a look at two excellent books: R. Bruce King's Beyond the Quartic Equation (1966) and Jerry M. Shurman's Geometry of the Quintic (CH, Oct'97). ^BSumming Up: Recommended. General readers; lower- and upper-division undergraduates. D. V. Feldman University of New Hampshire

Table of Contents

Introductionp. 1
1 The Scandal of the Irrationalp. 5
2 Controversy and Coefficientsp. 23
3 Impossibilities and Imaginariesp. 47
4 Spirals and Seashoresp. 59
5 Premonitions and Permutationsp. 73
6 Abel's Proofp. 85
7 Abel and Galoisp. 95
8 Seeing Symmetriesp. 111
9 The Order of Thingsp. 131
10 Solving the Unsolvablep. 145
Appendix A Abel's 1824 Paperp. 155
Appendix B Abel on the General Form of an Algebraic Solutionp. 171
Appendix C Cauchy's Theorem on Permutationsp. 175
Notesp. 181
Acknowledgmentsp. 203
Indexp. 205